[Imprint][Data Privacy Statement][E-Mail]

View long theorem info. View the proof. Back to main index. View the specification. View theorem base summary, View theorem base listing, the used properties by spec, the dependency list, the symbol table,

Proof step 35 from proof getInt-theorem (previous step)

0 ≤ band(b2i(by2), 255), band(b2i(by1), 255) < 256, 65536 * band(b2i(by2), 255) + 256 * band(b2i(by1), 255) < 16777216, 0 ≤ band(b2i(by1), 255) ⊦ bor(256 * band(b2i(by1), 255) + 65536 * band(b2i(by2), 255), bor(band(b2i(by0), 255), 16777216 * b2i(by3))) = bor(bytes2int(by3 ' + by2 ' + by1 ') * 256, band(b2i(by0), 255)), 16777216 * b2i(by3) + 256 * band(b2i(by1), 255) + 65536 * band(b2i(by2), 255) = bytes2int(by3 ' + by2 ' + by1 ') * 256, bor(256 * band(b2i(by1), 255) + 65536 * band(b2i(by2), 255), 16777216 * b2i(by3)) = bytes2int(by3 ' + by2 ' + by1 ') * 256

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 36:
⊦ bytes ≠ [] → bytes2int(bytes + by ') = bytes2int(bytes) * 256 + band(b2i(by), 255)
Proof step 37:
by3 ' + by2 ' ≠ [], 0 ≤ band(b2i(by2), 255), band(b2i(by1), 255) < 256, 65536 * band(b2i(by2), 255) + 256 * band(b2i(by1), 255) < 16777216, 0 ≤ band(b2i(by1), 255) ⊦ bor(256 * band(b2i(by1), 255) + 65536 * band(b2i(by2), 255), bor(band(b2i(by0), 255), 16777216 * b2i(by3))) = bor((bytes2int(by3 ' + by2 ') * 256 + band(b2i(by1), 255)) * 256, band(b2i(by0), 255)), 16777216 * b2i(by3) + 256 * band(b2i(by1), 255) + 65536 * band(b2i(by2), 255) = (bytes2int(by3 ' + by2 ') * 256 + band(b2i(by1), 255)) * 256, bor(256 * band(b2i(by1), 255) + 65536 * band(b2i(by2), 255), 16777216 * b2i(by3)) = (bytes2int(by3 ' + by2 ') * 256 + band(b2i(by1), 255)) * 256

Rule argument

name: bytes2int-rec rotate: F subst: [by, bytes] → [by1, by3 ' + by2 ']

Additional information

Used simplifier rules: ⊦ ¬ bytes + bytes0 ≠ [] ↔ bytes = [] ∧ bytes0 = [];% ⊦ by ' ≠ [];% ⊦ (bytes + bytes0) + bytes1 = bytes + bytes0 + bytes1; Used terms: by1, by3 ' + by2 '